Finding meaning in figures

Mathematics and statistics as a curriculum subject has always had a good grasp of context – the real world challenges that number crunching can help us solve. However, using context in the classroom not just to illustrate the purpose of statistical techniques but to actually deepen learning outcomes isn’t simple.

The New Zealand Curriculum states that “in a range of meaningful contexts, students will be engaged in thinking mathematically and statistically”.

“Seamlessly weaving context into the curriculum in a meaningful way can be challenging,” says Dr Sarah Howell, mathematics and statistics teacher at Wellington College, and teaching fellow of statistics at Victoria University of Wellington.

“However, the choice of meaningful contexts engages students and promotes other ideas in the curriculum such as key competencies and citizenship.”

Looking behind the data

Sarah recently spoke at the New Zealand Association of Mathematics Teachers Conference about using meaningful contexts for students using the statistical enquiry cycle at NCEA level 1.

She drew on findings from the trial at Wellington College of a curriculum resource she wrote to support NCEA achievement standard 1.10: ’Investigate a given multivariate data set using the statistical enquiry cycle’.

Titled Driven to Distraction, the curriculum resource is freely available from the NZTA education portal. It includes a multivariate data set and practice assessment to get students investigating how distractions and tiredness can impact on reaction times and the ability to carry out a task.

Sarah’s resource is also shared with teachers via the CensusAtSchool New Zealand website. CensusAtSchool’s Anne Patel says Driven to Distraction brings context to the front and centre of learning experiences, which will allow students to engage in the statistical tasks outlined in the resource.

“I believe many teachers need help and guidance to give their students the benefit of exploring contexts so they can really look behind the data and see the stories which statistical enquiry can reveal,” says Anne.

Sarah told conference attendees that choice of context matters in terms of student engagement. If they can find relevance in it, more students get hooked into an investigation. Students who don’t usually participate in discussion in the maths classroom can gain a voice as they have contributions to make about the context. Thoughtful engagement with realistic concerns also develops student key competencies, such as participating and contributing, and using language, symbols and text.

Several year 11 classes at Wellington College took part in a trial of Driven to Distraction. Teachers said the unit was well resourced to prepare students for achievement standard 1.10, and that it was good to have a meaningful context for students to investigate.

Brainstorming for context

Sarah says her own class was engaged after an initial brainstorm helped them understand the context of distractions while driving, and how factors such as tiredness or texting may be associated with reaction times.

“The discussion of the context set the scene and meant that students had the confidence to tackle the task, as any potential barriers of not understanding the context or variables of the statistical investigation had been removed.”

Students were then given the dataset, which comprises fictional but realistic data. Averages are consistent with research findings about texting and being tired.

The students posed a question, calculated statistics, drew appropriate comparative graphs and wrote analysis statements.

As part of their conclusion, students selected the evidence to back up the answer to their question, discussed how reasonable they thought their findings were and why friends who are learning to drive might be interested in these results. They also commented on what would happen if they took a different sample, confirming the robustness of their conclusion. The conclusion phase of enquiry thus built reflective statistical practice and gave time for students to think broadly as citizens, in line with the future focus principle of The New Zealand Curriculum.

“Students are taking away from this statistics investigation road safety messages about the issue of cell phone use during driving and the impact of being tired on concentration levels,” she says.

“They haven’t been explicitly told these messages; instead they’ve looked at the evidence and formed meaning for themselves from the data.”

And her own class linked their findings to their world in ways that she didn’t anticipate; for example, when it was suggested the impact on concentration levels of other distractions, such as eating, could be investigated, they discussed the types of foods they would likely eat while driving.

“When students personalise their investigations in ways we don’t anticipate as teachers, by linking their findings to their lives, you know that they’re not just telling you what they think you want to hear but have formed a deeper understanding of the data.”

Inside the maths and statistics resource

The resource has four components:

An outline, which includes links to online resources related to the context, especially the effects of distractions and fatigue.

A practice assessment for students.

A data set consisting of a sample of 120 reaction test and typing test results, with two categorical variables (tiredness and reading a text message). The data set comes as an Excel spreadsheet and a CSV file.

Three PowerPoint presentations for classroom use. Teachers can use these to model how to pose questions, analyse the data and write conclusions.

This and other resources by Dr Sarah Howell can be downloaded here: www.education.nzta.govt.nz/resources/secondary/mathematics.

Support for secondary literacy and numeracy

Curriculum writer Pam Hook has just revised a resource that uses the context of young drivers and safe road use to support NZQA literacy and numeracy requirements.

Practising active citizenship through safer journeys can be freely downloaded and modified by teachers. It is housed on the NZTA education portal.

Learning experiences provide evidence for assessment for these unit standards:

26622: Write to communicate ideas for a purpose and audience

26624: Read texts with understanding

26625: Actively participate in spoken interactions

26623: Use numbers to solve problems

26626: Interpret statistical information for a purpose

26627: Use measurement to solve problems

The resource has learning experiences that use The Official New Zealand Road Code to integrate learning for citizenship within relevant contexts for secondary students. Activities include how to check a car is safe before getting in, discussions about the reasons for road rules, route planning, identifying hazards, reflecting on attitudes, creating a whakataukī (proverb) and writing to a politician.

Teachers can consider the interests, current abilities and future needs of students when selecting suitable activities to include. Each activity is backed by links to sections of the road code and to road safety modules in Pathways Awarua, the online literacy and numeracy skills programme.